Related papers: Accurate calculation of eigenvalues and eigenfunct…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
In this paper we are concerned to find the eigenvalues and eigenvectors of a real symetric matrix by applying a new numerical method similar to Jacobi method. Our approch consists to use a new orthogonal matrix. The computation of the…
In this work, we propose a method combining the Sinc collocation method with the double exponential transformation for computing the eigenvalues of the anharmonic Coulombic potential. We introduce a scaling factor that improves the…
We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…
In the present article, we describe a method of introducing the harmonic potential into the Klein-Gordon equation, leading to genuine bound states. The eigenfunctions and eigenenergies are worked out explicitly.
The energy eigenvalues of the anharmonic oscillator characterized by the cubic potential for various eigenstates are determined within the framework of the hypervirial-Pad\'e summation method. For this purpose the E[3,3] and E[3,4] Pad\'e…
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…
The eigenvalues of a pure quartic oscillator are computed, applying a canonical operator formulation, generalized from the harmonic oscillator. Solving a 10x10 secular equation produces eigenvalues in agreement, to at least 4 significant…
In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. It is illustrated through the particular cases of the harmonic oscillator and the Coulomb potential. In this kind of system the…
In this paper we consider eigenvalues asymptotics of the energy operator in the one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator of this…
We obtain the eigenvalues and eigenfunctions of the singular harmonic oscillator $V(x)=\alpha/(2x^2)+x^2/2$ by means of the simple and straightforward Frobenius (power-series) method. From the behaviour of the eigenfunctions at origin we…
Using the technique of tridiagonal representation approach; for the first time, we extend this method to study quantum systems with literally perturbed Hamiltonians. Specifically, we consider a quantum system in a 3D spherical oscillator…
An infinite sequence of potential well functions is considered. A numerical method is used for the Schr$\ddot{\text{o}}$dinger equation to obtain the energy eigenvalue spectra for a number of these potential well functions. The results for…
A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates {\em nonuniform} and optimal spatial discretization.…
An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
We apply the effective potential analytic continuation (EPAC) method to one-dimensional asymmetric potential systems to obtain the real time quantum correlation functions at various temperatures. Comparing the EPAC results with the exact…
The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent…
There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of…
We analyse some PT-symmetric oscillators with $T_{d}$ symmetry that depend on a potential parameter $g$. We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of $g$. Pairs of…